For example, if you want to find the fifth number in the sequence, your table will have five rows. When using the table method, you cannot find a random number farther down in the sequence without calculating all the number before it. For example, if you want to find the 100th number in the sequence, you have to calculate the 1st through 99th numbers first. This is why the table method only works well for numbers early in the sequence.

The term refers to the position number in the Fibonacci sequence. For example, if you want to figure out the fifth number in the sequence, you will write 1st, 2nd, 3rd, 4th, 5th down the left column. This will show you what the first through fifth terms in the sequence are.

The correct Fibonacci sequence always starts on 1. If you begin with a different number, you are not finding the proper pattern of the Fibonacci sequence.

Remember, to find any given number in the Fibonacci sequence, you simply add the two previous numbers in the sequence. To create the sequence, you should think of 0 coming before 1 (the first term), so 1 + 0 = 1.

1 + 1 = 2. The third term is 2.

1 + 2 = 3. The fourth term is 3.

2 + 3 = 5. The fifth term is 5.

This is a closed formula, so you will be able to calculate a specific term in the sequence without calculating all the previous ones. This formula is a simplified formula derived from Binet’s Fibonacci number formula. [8] X Research source The formula utilizes the golden ratio (ϕ{\displaystyle \phi }), because the ratio of any two successive numbers in the Fibonacci sequence are very similar to the golden ratio. [9] X Research source

For example, if you are looking for the fifth number in the sequence, plug in 5. Your formula will now look like this: x5{\displaystyle x_{5}}=ϕ5−(1−ϕ)55{\displaystyle {\frac {\phi ^{5}-(1-\phi )^{5}}{\sqrt {5}}}}.

For example, if you are looking for the fifth number in the sequence, the formula will now look like this: x5{\displaystyle x_{5}}=(1. 618034)5−(1−1. 618034)55{\displaystyle {\frac {(1. 618034)^{5}-(1-1. 618034)^{5}}{\sqrt {5}}}}.

In the example, the equation becomes x5{\displaystyle x_{5}}=(1. 618034)5−(−0. 618034)55{\displaystyle {\frac {(1. 618034)^{5}-(-0. 618034)^{5}}{\sqrt {5}}}}.

In the example, 1. 6180345=11. 090170{\displaystyle 1. 618034^{5}=11. 090170}; −0. 6180345=−0. 090169{\displaystyle -0. 618034^{5}=-0. 090169}. So the equation becomes x5=11. 090170−(−0. 090169)5{\displaystyle x_{5}={\frac {11. 090170-(-0. 090169)}{\sqrt {5}}}}.

In the example, 11. 090170−(−0. 090169)=11. 180339{\displaystyle 11. 090170-(-0. 090169)=11. 180339}, so the equation becomes x5{\displaystyle x_{5}}=11. 1803395{\displaystyle {\frac {11. 180339}{\sqrt {5}}}}.

In the example problem, 11. 1803392. 236067=5. 000002{\displaystyle {\frac {11. 180339}{2. 236067}}=5. 000002}.

If you used the complete golden ratio and did no rounding, you would get a whole number. It’s more practical to round, however, which will result in a decimal. [12] X Research source In the example, after using a calculator to complete all the calculations, your answer will be approximately 5. 000002. Rounding to the nearest whole number, your answer, representing the fifth number in the Fibonacci sequence, is 5.